STAT 400 Lecture AL1 Spring 2015 Dalpiaz Homework 1 due Friday January 30 by 3 00 p m Please include your name with your last name underlined your NetID and your discussion section number at the top of the first page Do NOT use a computer You may only use and 1 4 on a calculator Show all work 1 Evaluate the following integrals a 2 x e 3 x dx b 2 x sin x dx 0 0 c x 1 x 4 dx 1 2 Let c 0 Consider f x y x c y and A x y 0 y x 1 a Sketch A That is sketch x y 0 y x 1 b Set up the double integral s of f x y over A with the outside integral w r t x and the inside integral w r t y c Set up the double integral s of f x y over A with the outside integral w r t y and the inside integral w r t x d Find the value of c such that f x y dx dy A 1 3 Consider f x y x y 3 and A x y 0 y 1 y x 2 a Sketch A That is sketch x y 0 y 1 y x 2 b Set up the double integral s of f x y over A with the outside integral w r t x and the inside integral w r t y c Set up the double integral s of f x y over A with the outside integral w r t y and the inside integral w r t x d Use either b or c to evaluate f x y dx dy A 4 Evaluate the following sums do NOT use a calculator a k 3 2 5k b 0 6 2 k 1 c k 1 5 Suppose P A 0 70 a Find P A B 6 Suppose b P A 0 40 P A B 0 19 2k k 5 Find P A B P A C 0 25 P A B 0 80 P B 0 50 P B 0 34 k c Find P A B P C 0 55 P B C 0 17 P A B C 0 07 a Find P A B C c Find P A B C 7 Let a 1 Suppose S 2 3 4 5 6 and P k a Find the value of b Find P outcome is odd c Find P outcome is less than or equal to 5 c b Find P A B C c k 2 3 4 5 6 ak that makes this is a valid probability distribution 8 Suppose S 2 3 4 5 6 and a Find the value of b Find P outcome is greater than or equal to 5 9 A family that owns two automobiles is selected at random Suppose that the c P k c 2k k k 2 3 4 5 6 that makes this is a valid probability distribution probability that the older car is American is 0 80 the probability that the newer car is American is 0 70 and the probability that both the older and the newer cars are American is 0 60 a Find the probability that at least one car is American i e that either the older car or the newer car or both cars are American b What is the probability that the newer car is American given that the older car is American c What is the probability that the newer car is American given that the older car is not American 10 At Anytownville College 25 of all students are enrolled in an introductory level statistics class and 20 of all students are seniors It is also known that 15 of the seniors are enrolled in an introductory level statistics class a Initech is offering an internship to a Anytownville College student who is either a senior or is enrolled in an introductory level statistics class or both What proportion of Anytownville College students are eligible for this internship b What proportion of students enrolled in an introductory level statistics class at Anytownville College are seniors c Given that a student selected at random is not a senior what is the probability that he she is enrolled in an introductory level statistics class
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